This article describes some ways to set up player monologues.
By default, the Dialogue Manager GameObject's Display Settings > Input Settings > Always Force Response Menu checkbox is ticked. When this checkbox is ticked and the conversation is at a point where only player dialogue entries are available, the Dialogue System will always show a response menu, even if there is only one dialogue entry to show in the menu. (A player dialogue entry is an entry assigned to an actor whose Is Player checkbox is ticked.)
If you want single player entries to play automatically as subtitles, untick Always Force Response Menu. Then tick Subtitle Settings > Show PC Subtitles During Line if it's not already ticked.
If you only want Always Force Response Menu to apply to a specific conversation, then instead of changing the Dialogue Manager's settings, inspect the conversation's properties. (In the Dialogue Editor's Conversations section, select Menu > Conversation Properties.) Tick Override Display Settings > Input Settings, and untick Always Force Response Menu there.
In addition, you can include the markup tags [f] and [auto] in your Dialogue Text or Menu Text to control individual entries. If a player entry contains [f], it will force the entry to appear in a response menu. If it contains [auto], it will automatically choose that entry and show it as a subtitle even if other player entries are also available -- in other words, it will bypass the response menu.
Another way to play a monologue is to create a separate actor, named something like Monologue or Narrator, and leave its Is Player checkbox unticked. Then use this actor for the monologue conversation. This is useful if you want to always use a different dialogue UI or subtitle panel for monologue conversations, since you can create a corresponding Monologue/Narrator GameObject and add an Override Dialogue UI component or a Dialogue Actor component that uses a different subtitle panel.